The generator matrix

 1  0  0  1  1  1  0 X^3  1  1 X^3 X^2  1  1  1  1 X^3+X X^3+X  1 X^3+X  1  1  1 X^3+X^2+X  1 X^2+X X^3+X^2  1  1  1 X^3+X^2+X  1  1  1 X^3+X X^3+X  1  X X^2  1  1  1 X^2  1 X^3  1  X X^3  X  1 X^3+X^2  1  X  1  X  1  1 X^3+X^2 X^2+X  1 X^3+X^2+X X^3+X^2  1  1 X^3  1 X^3  1  1  1 X^3+X  1  1 X^3+X^2+X  1 X^3+X^2+X  1  1  1
 0  1  0  0 X^2+1 X^2+1  1 X^3+X^2+X X^3 X^3+X^2+1  1  1 X^3+X^2  1 X^2+X X+1  1 X^2+X  X  1 X^3+X+1 X^3+X^2+X+1 X^2+X+1  0 X^3+X^2  1  1 X^3 X^3+X^2 X^3+X+1  1 X^3+X^2+X X^3+X  X X^3+X  1 X^2+X  1  1  1 X^3+X^2+X+1 X^2+1  0 X^3+X^2+1  1 X^3+1  1 X^3+X  1  X  1 X^2 X^3+X^2 X^3+1  1 X^2+X+1 X^2+1  1 X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3+X X^2+X  1 X+1  1 X^2+X+1 X^3 X^3+X^2+X+1  1  0 X^2  1  1  1 X^3+X^2+X X^2+X  0
 0  0  1 X+1 X^3+X+1 X^3 X^3+X^2+X+1  1 X^3+X^2+X X^2+1  1 X^3+X X^3+X^2+1  X X^3+X+1 X^2 X^3+X^2+1  1  X X^3+X^2+X X^2+X+1 X^3+X^2+X X^2+1  1 X+1  0 X^2+1 X^3+X^2  1 X^3+X X^2+X+1 X^3+X^2 X^3+X^2 X^3+X^2+X+1  1 X^2 X^3+X^2+1  1  0 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+1  1 X^2 X^3+X^2+1 X^2+X+1 X^3+X^2+X  1 X+1 X^3+X^2+1 X^3+X X^3+X^2+X  1 X^3 X^3+X^2+X+1 X^3+X X^3+1 X^3+X^2+X+1  1 X^3+X^2+X  1  1 X^3+X^2+1 X^3+X^2+X X^3+X X^3 X+1  X X^2+X X^3+X^2  1  1 X^2+1 X^3+X X^3+X^2+X X^2+1 X^3+X^2+X+1  1  0
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3  0  0  0  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+113x^74+780x^75+854x^76+1278x^77+956x^78+1124x^79+767x^80+768x^81+415x^82+420x^83+208x^84+254x^85+104x^86+92x^87+25x^88+20x^89+10x^90+2x^94+1x^96

The gray image is a linear code over GF(2) with n=632, k=13 and d=296.
This code was found by Heurico 1.16 in 3.41 seconds.